Simple and Compound Interest - meaning and formulas

Simple and compound interest 

Simple interest is the money that is paid only on an original amount of money that has been borrowed or invested, and not on the extra money that the original amount earns.

Simple interest or SI = (P*T*R)/100

P is the principal (the money borrowed or lent out for a certain period) .  

R is the interest rate (the rate at which the interest has to be calculated) .

T is the time (the period for which the principal was borrowed) .

Amount is the summation of principal and simple interest .

A = P + SI

There's another way to calculate the amount .

A = P [ 1 + TR/100 ]

Let's calculate the simple interest for the following problem.

Principal amount = 10000
Time = 2 years
Rate of interest = 5% per annum

Sol. 

Let's get to the compound interest (CI) .

Compound interest is the  interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan .

To calculate the CI we need to first compute the total amount when the CI is accumulated with the principal .
So ,to calculate this amount we use the following formula :



After we ascertain the amount ,we can calculate the CI by using the following formula :


CI = A - P

The basic concept of CI is that interest is added back to the principal sum so that interest is earned on that added interest during the next compounding period .

To the right is another formula to calculate the CI(compound interest). 

Let's take a look at how this works.

A man deposits Rs 1000 in a savings account at an interest rate of 10% per annum. At the end of one year he will get Rs 100 interest on his deposit. However, unless he takes out his Rs 100 in cash, it will be added to his original Rs 1000. Thus, if he leaves his money in his account, in the next year the bank will be paying him interest on his original Rs 1000 plus the Rs 100 interest,i.e.,Rs 1100. In the third year the interest will once again be added to the new principal of Rs 1100, and so on for as long as the money is left in the account.

This kind of interest is known as compound interest.


Now let's calculate the compound interest for the following problem.

P = 1000
R = 10%p.a.
T = 5 years

Sol.